Aptitude - Pipes and Cistern - Discussion

So simple.

a =60; b= 40; a+b = 60*40/60+40 = 24 (formula).

Let's take tank capacity 2x min (i.e x+x).

x/40 + x/24 = 1 (full tank).

By solving, we get x = 15 min.

Therefore 2x = 2*15 = 30 min.

By LCM method I am getting different answer.

A = 60 min.
B = 40 min.

By taking LCM total work is 120 unit.

So A does 120/60 = 2 unit.

B does 120/40 = 3 unit.

Together 5 unit so time taken by both A and B to complete work is 120/5 = 24 min.

It means B will work alone for 12 min and work done by B is 12x3 = 36 unit.

Remaining work is 120-36 = 84 unit which is done by both A and B so 84/5 = 16.8 min.

Then total time taken is = 12+16.8 = 28.8 min.

@Madhu.

Here you are considering that B does half of work but in question they had mention only the half of time B does the work. Please clarify my doubt.

Here in this question they give a = 60, b = 40.

Then half of the b is = 20.

After half of the a and b that means a+b/2 = 60+40/2 = 50.

Then, 50-20 = 30.

@Salini.

I completely agree to your let method and the what question is saying. But through LCM method also answer would be 28 min 48 seconds.

@suresh.

What you explained was very simple & easy to understand. But in the question its mentioned leaking the Time taken by pipe (B) & time taken by both pipes (A+B). So how can we subtract 50-20?

Mine answer is coming 32 mins. By LCM method I am getting different answer.

A = 60 min.

B = 40 min.

By taking LCM total work is 120 unit. (say litre).

So a fills the tank in 120/60 = 2 litre/min.

B does it in 120/40 = 3 litre/min.

Together 5 litres. So time taken by both a and b to complete work is 120/5 = 24 min.

Now half tank means capacity of 60 litres. (60+60=120).

Now half the tank is filled by a+b=60/ (3+2) =12 min.

And half the tank is filled by b only = 60/3=20 min.

So therefore, 12+20=32 min.

L.C.M of 40 and 60 is 120.

So A's rate of work is 2 and B's rate of work is 3.

Hence now B work for half of time an A+B for another half.

So, 3x+(2x3)x = 120.

Hence x = 15 which is half time hence full time is 2x = 2x15 = 30 min.

@Vinayak.

How will you multiply (2*3) you need to add them?

1st tape can fill half of the tank in 3 hours.

Remaining part = 1-1/2 = 1/2 part.

Now 4 tape can fill the tank in 1 hour = 4*1/6 = 2/3.

Now,
2/3 parts fill in 1 hour.
1/2 parts fill in 1*3/2*2 = 45 mins.

So, total time = 3hrs+45mins = 3 hours 45 mins.